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A 2D Advancing-Front Delaunay Mesh Refinement Algorithm.

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This study introduces an improved Delaunay mesh refinement algorithm. The new method generates size-optimal meshes with better minimum angles, especially for planar straight line graphs (PSLG).

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Area of Science:

  • Computational Geometry
  • Mesh Generation
  • Computer-Aided Design

Background:

  • Delaunay mesh refinement is crucial for accurate simulations.
  • Existing algorithms have limitations on minimum angles and performance with small input angles.
  • Chew's first algorithm provides a foundation for Delaunay mesh refinement.

Purpose of the Study:

  • To generalize Chew's first algorithm for Delaunay mesh refinement.
  • To improve the quality of generated meshes, specifically focusing on minimum angles.
  • To handle planar straight line graphs (PSLG) efficiently.

Main Methods:

  • Splitting line segments of a PSLG proportionally to local feature size.
  • Refining Delaunay triangulations by inserting off-center Steiner vertices.
  • Prioritizing triangles with the shortest edges using an advancing front approach.

Main Results:

  • Achieved size-optimal, truly or constrained Delaunay meshes with minimum angles < 30° (without small input angles).
  • Improved minimum angles compared to prior algorithms (26.4° and 28.6°).
  • Reduced the upper bound on the maximum angle to > 120° (improvement from ~137°).

Conclusions:

  • The generalized algorithm offers superior mesh quality, particularly regarding minimum angles.
  • The method effectively refines meshes for PSLGs, even with small input angles.
  • This advancement contributes to more accurate and reliable computational simulations.